Using a monotonic density ratio model to find the asymptotically optimal combination of multiple diagnostic tests

To achieve optimal sensitivity and specificity, one needs to combine different diagnostic tests. The celebrated Neyman–Pearson lemma enables us to use the density ratio to optimally combine different diagnostic tests.

In this paper, we propose a semiparametric model by directly modeling the density ratio between the diseased and nondiseased population as an unspecified monotonic nondecreasing function of a linear or nonlinear combination of multiple diagnostic tests. This method is appealing in that it is not necessary to assume separate models for the diseased and nondiseased populations. Further, the proposed method provides an asymptotically optimal way to combine multiple test results.